As modern control theory attempts to elucidate the complexity of systems that combine differential equations and event-driven logic, it must overcome challenges having to do with limited expressive power as well as practical difficulties associated with translating control algorithms into robust and reusable software. The Motion Description Language (MDL) and its ``extended' counterpart MDLe, have been at the center of an ongoing effort to make progress on both of these fronts. The goal of this paper is to define MDLe as a formal language, thereby connecting with the vast literature on the subject, and to stimulate experimental work. We discuss the expressive power of MDLe and provide some examples of MDLe programs. <p> This work has appeared in the Proceedings of the 41st IEEE Conference on Decision and Control, 2002.